Higher Spin Alternating Sign Matrices

We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The case r=1 gives standard alternating sign matrices, while the case in which all matrix entries are nonnegative gives semimagic squares. We show that the higher spin alternating sign matrices of size n are the integer points of the r-th dilate of an integral convex polytope of dimension (n-1)^2 whose vertices are the standard alternating sign matrices of size n. It then follows that, for fixed n, these matrices are enumerated by an Ehrhart polynomial in r.Comment: 41 pages; v2: minor change

Using a theory of mind to find best responses to memory-one strategies

Memory-one strategies are a set of Iterated Prisoner's Dilemma strategies that have been praised for their mathematical tractability and performance against single opponents. This manuscript investigates best response memory-one strategies with a theory of mind for their opponents. The results add to the literature that has shown that extortionate play is not always optimal by showing that optimal play is often not extortionate. They also provide evidence that memory-one strategies suffer from their limited memory in multi agent interactions and can be out performed by optimised strategies with longer memory. We have developed a theory that has allowed to explore the entire space of memory-one strategies. The framework presented is suitable to study memory-one strategies in the Prisoner's Dilemma, but also in evolutionary processes such as the Moran process, Furthermore, results on the stability of defection in populations of memory-one strategies are also obtained

Using a theory of mind to find best responses to memory-one strategies

Memory-one strategies are a set of Iterated Prisoner’s Dilemma strategies that have been praised for their mathematical tractability and performance against single opponents. This manuscript investigates best response memory-one strategies with a theory of mind for their opponents. The results add to the literature that has shown that extortionate play is not always optimal by showing that optimal play is often not extortionate. They also provide evidence that memory-one strategies suffer from their limited memory in multi agent interactions and can be out performed by optimised strategies with longer memory. We have developed a theory that has allowed to explore the entire space of memory-one strategies. The framework presented is suitable to study memory-one strategies in the Prisoner’s Dilemma, but also in evolutionary processes such as the Moran process. Furthermore, results on the stability of defection in populations of memory-one strategies are also obtained

Gemini and Lowell observations of 67P/Churyumov−Gerasimenko during the <i>Rosetta</i> mission

We present observations of comet 67P/Churyumov−Gerasimenko acquired in support of the Rosetta mission. We obtained usable data on 68 nights from 2014 September until 2016 May, with data acquired regularly whenever the comet was observable. We collected an extensive set of near-IR J, H and Ks data throughout the apparition plus visible-light images in g', r', i' and z' when the comet was fainter. We also obtained broad-band R and narrow-band CN filter observations when the comet was brightest using telescopes at Lowell Observatory. The appearance was dominated by a central condensation and the tail until 2015 June. From 2015 August onwards, there were clear asymmetries in the coma, which enhancements revealed to be due to the presence of up to three features (i.e. jets). The features were similar in all broad-band filters; CN images did not show these features but were instead broadly enhanced in the southeastern hemisphere. Modelling using the parameters from Vincent et al. replicated the dust morphology reasonably well, indicating that the pole orientation and locations of active areas have been relatively unchanged over at least the last three apparitions. The dust production, as measured by A(0°)fρ peaked ∼30 d after perihelion and was consistent with predictions from previous apparitions. A(0°)fρ as a function of heliocentric distance was well fitted by a power law with slope −4.2 from 35 to 120 d post-perihelion. We detected photometric evidence of apparent outbursts on 2015 August 22 and 2015 September 19, although neither was discernible morphologically in this data set

A bibliometric study of research topics, collaboration, and centrality in the iterated prisoner's dilemma

This manuscript explores the research topics and collaborative behaviour of authors in the field of the Prisoner’s Dilemma using topic modeling and a graph theoretic analysis of the co-authorship network. The analysis identified five research topics in the Prisoner’s Dilemma which have been relevant over the course of time. These are human subject research, biological studies, strategies, evolutionary dynamics on networks and modeling problems as a Prisoner’s Dilemma game. Moreover, the results demonstrated the Prisoner’s Dilemma is a field of continued interest, and that it is a collaborative field compared to other game theoretic fields. The co-authorship network suggests that authors are focused on their communities and that not many connections across the communities are made. The most central authors of the network are the authors connected to the main cluster. Through examining the networks of topics, it was uncovered that the main cluster is characterised by the collaboration of authors in a single topic. These findings add to the bibliometrics study in another field and present new questions and avenues of research to understand the reasons for the measured behaviours

Modelling deadlock in open restricted queueing networks

Open restricted queueing networks give rise to the phenomenon of deadlock, whereby some customers may be unable to ever leave a server due to mutual blocking. This paper explores deadlock in queueing networks with limited queueing capacity, presents a method of detecting deadlock in discrete event simulations, and builds Markov chain models of these deadlocking networks. The three networks for which Markov models are given include single and multi-server networks for one and two node systems. The expected times to deadlock of these models are compared to results obtained using a simulation of the stochastic process, together with the developed deadlock detection method. This paper aims to be of value to simulation modellers of queues